In this chapter, the problem of stability analysis is presented for 2-D Markov jump systems in the Roesser model with interval delays and uncertain transition rates. Specifically, it is assumed that transition probabilities of the jumping process driven by a Markov chain are not exactly known but can be estimated by prescribed ranges. Inspired by the conventional Lyapunov–Krasovskii functional method, an analysis scheme for the stochastic stability property is first developed. The proposed scheme is then utilized in combination with weighted 2-D summation inequalities to derive delay-dependent stochastic stability conditions in terms of linear matrix inequalities for 2-D Markov jump Roesser systems with interval delays. Numerical examples are given to illustrate the effectiveness of the obtained results.

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Stability of Two-Dimensional Time-Delay Roesser Systems with Markovian Switchings

  • Le Van Hien

摘要

In this chapter, the problem of stability analysis is presented for 2-D Markov jump systems in the Roesser model with interval delays and uncertain transition rates. Specifically, it is assumed that transition probabilities of the jumping process driven by a Markov chain are not exactly known but can be estimated by prescribed ranges. Inspired by the conventional Lyapunov–Krasovskii functional method, an analysis scheme for the stochastic stability property is first developed. The proposed scheme is then utilized in combination with weighted 2-D summation inequalities to derive delay-dependent stochastic stability conditions in terms of linear matrix inequalities for 2-D Markov jump Roesser systems with interval delays. Numerical examples are given to illustrate the effectiveness of the obtained results.